Problem: What is the inverse of the function $h(x)=\dfrac{3}{2}(x-11)$ ? $h^{-1}(x)=$
Answer: Let's start by replacing $h(x)$ with $y$. $y=\dfrac{3}{2}(x-11)$ If a function contains the point $(a,b)$, the inverse of that function contains the point $(b,a)$. So if we swap the position of $x$ and $y$ in the equation, we get the inverse relationship. In this case, the function is $y=\dfrac{3}{2}(x-11)$, so the inverse relationship is $x=\dfrac{3}{2}(y-11)$. Solving this equation for $y$ will give us an expression for $h^{-1}(x)$. $\begin{aligned} x&=\dfrac{3}{2}(y-11)\\\\ \dfrac{2}{3}x&=y-11\\\\ \dfrac{2}{3}x+11&=y\\\\\\ \end{aligned}$ The inverse of the function is $h^{-1}(x)=\dfrac{2}{3}x+11$. [I saw someone solve this problem by originally solving for x. Were they wrong?]